Problem: Simplify the following expression: $ r = \dfrac{-n - 5}{10n} - \dfrac{-7}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-n - 5}{10n} \times \dfrac{5}{5} = \dfrac{-5n - 25}{50n} $ Multiply the second expression by $\dfrac{10n}{10n}$ $ \dfrac{-7}{5} \times \dfrac{10n}{10n} = \dfrac{-70n}{50n} $ Therefore $ r = \dfrac{-5n - 25}{50n} - \dfrac{-70n}{50n} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-5n - 25 + 70n }{50n} $ Distribute the negative sign: $r = \dfrac{-5n - 25 + 70n}{50n}$ $r = \dfrac{65n - 25}{50n}$ Simplify the expression by dividing the numerator and denominator by 5: $r = \dfrac{13n - 5}{10n}$